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Mastering Calculus Techniques: Logs, Exponentials, and Transcendental Functions

Explore advanced calculus topics including integrals of reciprocal functions, logarithmic differentiation, and growth/decay problems. Learn how to simplify logs, solve exponential equations, and apply derivatives/integrals to trig functions. Practice the Second Fundamental Theorem of Calculus and separation of variables for quick solutions. Understand the distinction between derivatives and integrals, and apply differentiation/integration methods effectively. Solve population problems and exponential growth/decay scenarios. Enhance your calculus skills with this comprehensive guide.

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Mastering Calculus Techniques: Logs, Exponentials, and Transcendental Functions

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  1. Ch. 6 Review AP Calculus

  2. 6.2: Integrals of Reciprocal Functions • 6.2: Second Fundamental Theorem of Calculus • 6.3: Log Properties (The Big Four) • 6.4: Solving Exponential Equations (logs) • 6.4: Logarithmic Differentiation (exponential functions) • Growth/Decay Problems (using logs to solve)… including Separation of Variables • Derivatives/Integrals of Transcendental Functions (trig, exponential, logs) Topics

  3. If f(x) =, find f’(x). • If g(x) = , find g’(x). • Example 8, pg. 276 Second Fundamental Theorem of Calculus

  4. Integrating Reciprocal Functions

  5. 3 log 2 ln Simplifying Logs

  6. Derivatives of Logs/Logarithmic Differentiation

  7. Find f’(x) if Derivatives of Logs/Logarithmic Differentiation

  8. Power Rule, Chain Rule • Product Rule, Quotient Rule • e^x 5^x ln x Differentiation/Integration Methods

  9. Trig Integrals

  10. See Population Problem, pg. 269. • We now know how to solve this QUICKLY!!! Separation of Variables

  11. Know how to substitute given values into R(t) = formula. • Be able to recognize derivative (rate of change, instantaneous rate, slope of tangent, etc.) vs. integral (sum, area under curve, total accumulation). Exponential Growth/Decay

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